Chasing Time's Arrow

Why does time run from past to future? How are past and future different? These deep philosophical questions are the subject of this brief book. According to its publisher, it aims to be a kind of "elementary textbook . . . accessible to interested high-school students" as well as "an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level." These goals are ambitious, but not impossible. Some works explain the elements and also give penetrating insights; one thinks of Henri Poincaré, Hermann Weyl and Richard Feynman.

David Z. Albert, a professor of philosophy at Columbia University, presents thought-provoking ideas in Time and Chance, including Poincaré's fascinating theorem about endless recurrence. But Albert wants to do more than review established concepts; he wants to present a novel view of irreversibility. He treats the difference between past and future as resting not only on laws of motion and statistical inference but also on what he calls the "past-hypothesis," namely that the universe began in some highly condensed state (for instance, just after the big bang). Albert also speculates that quantum mechanics may be ultimately responsible for the irreversibility of time.

Although it contains interesting material, this book does not really meet its aims. Only an extraordinary high-school student could follow its dense argument, which requires strenuous effort even from a well-versed reader. Albert tries hard but makes some unfortunate stylistic choices. Trying to be fresh and accessible, he adopts an informal writing style meant to evoke an engaging spoken voice. Many sentences are fragments that begin with "and," contain lots of italicized phrases or are quite loosely constructed. What might have been idiomatic speech comes out as somewhat convoluted writing. Albert is given to interjecting "Good," the nervous tic of a lecturer assuring himself that all is well, or "Period," as if to dismiss further questions.

Indeed, Albert aims at definitive views, often differing markedly from common accounts of irreversibility and statistical mechanics. As he puts it, "What can all those guys have been up to?" He is out to set "those guys" straight but doesn't often inquire why they had those views. His own arguments tend not to be persuasive because of basic questions that need further clarification and rethinking.

For instance, Albert takes issue with the common wisdom that Maxwell's electromagnetic equations are reversible in time. He notes, correctly, that those equations are reversible if one considers only the motions of particles, but not if one considers separately the values of electric and magnetic fields. If time flowed backward, the magnetic field would be reversed. Yet he does not note that this would require that the currents that produced the field flow backward. If we consider the field and its sources, Maxwellian electrodynamics turns out to be time-reversible after all.

Albert's arguments would have been strengthened by asking more such questions, rather than trying to answer them prematurely. It is also not clear how the "past-hypothesis" relates to such classic formulations as Ludwig Boltzmann's insistence on the importance of the initial conditions (as opposed to the equations of motion). Despite the importance of the past, Albert gives scarcely any discussion of the historical emergence of these ideas. This allows more space for presentation of his own ideas but deprives the reader of help in considering alternative views. I count only a dozen specific citations in the text, most of them recent; there is no bibliography to guide those who would like to explore these matters further.

To think about these issues for themselves, readers need more help grasping and assessing such difficult ideas. These deep questions call for the most balanced dialogue possible. Philosophy may well aspire to set physics straight, yet it cannot escape the haunting question of Socrates: "But is it really true?"—Peter Pesic, St. John's College, Santa Fe, New Mexico